In the U.S., to hash out is to have a discussion, especially one meant to arrive at a deal or a resolution. The corresponding phrase outside North America is thrash out, which is used almost exactly the same way. Hash out is the preferred term in Canada, but thrash out is more common in Canadian publications than in U.S. ones, where it is almost nonexistent.
Both hash out and thrash out usually take a direct object, and the object can be either the problem in need of resolution (e.g., “we hashed out our differences and came to an agreement”) or the result of the discussion (e.g., “we discussed our differences and thrashed out an agreement”).
Whether the two terms have a shared source is not clear. The origins of thrash out are obvious; it extends metaphorically from the thrashing (also spelled threshing) process in agriculture, which involves separating the edible part of grain from the chaff. Hash out perhaps descends from the older phrasal verb hash over, which refers to the culinary practice of making meals out of chopped-up pieces. Figuratively, to hash something over is to hastily assemble it out of small elements at hand, and this is not far from the meaning of hash out. It could be that hash over evolved into hash out under influence thrash out, which used to be more common in the U.S. than it is now.
Thrash out in the figurative sense has been in use in British English since the 19th century (examples predating ours can be found in the Oxford English Dictionary, whose oldest is from 1882, and elsewhere):
The general question of motor car v. electric locomotive has been thrashed out a good deal lately. [Electrical Review (1898)]
[I]f we could bring them together in a committee to thrash out a detailed scheme, it would be possible to have something more practical than anything we have yet seen on this subject. [Speech by South African Jan Smuts published in European War pamphlets (1917)]
They had, therefore, to examine and thrash out the achievements of the past six months before they could proceed to prepare for the new campaign. [The Whig Party: 1807-1812, Michael Roberts (1965)]
Or what about the correspondence with Alfred Russel Wallace, in which the two scientists thrashed out the individual/group selection alternatives? [New Scientist, 1988)]
Mr Letwin has been taking the lead on behalf of the government to thrash out proposals for future regulation of the press. [Financial Times (2013)]
The American hash out emerged in the early 20th century and was common by midcentury:
I sure was glad to see him and when leaving him as train pulled out I promised to return and hash out some of the troubles we went through years ago. [letter to Plumbers, Gas and Steam Fitters Journal (1917)]
“Hold on, Judge. That sounds like sense. Let’s get some folks together and hash it out.” [Belligerent Peter, David De Forest Burrell (1920)]
I’ll go in tomorrow morning, and we can sit down and hash it out together. [A Collection of Strangers, Dolores Hitchens (1970)]
Major league baseball owners gathered today with hopes of firming up their television future by hashing out a proposed joint venture with ABC and NBC. [New York Times (1993)]
New York City and its teachers union haven’t met for more than three weeks to hash out a deal on a new teacher-evaluation system. [Wall Street Journal (2013)]